Position racks in the upper and lower thirds of the oven; preheat broiler. Working in batches, transfer the potatoes and onion to a towel; wring out liquid and transfer to a medium bowl. Stir in the eggs, matzo meal, baking powder and salt and pepper.

In a medium ovenproof skillet, melt 1 tbsp. butter over medium-low heat. Spoon half (about 1 cup) of the potato mixture into the skillet. Using a spatula, flatten the mixture into a 6-inch disk. Cook, turning once, until golden-brown and crisp, 5 to 7 minutes. Transfer the latke to a cooling rack set inside a baking sheet. Repeat with the remaining butter and potato mixture. Keep the latkes warm on the lower oven rack.

In the same skillet, arrange the meat in an even layer; scatter the sauerkraut on top. Cover; cook over medium until heated through, 2 to 3 minutes. Top with the cheese; broil until melted, about 2 minutes.

Spread the Russian dressing on one of the latkes; top with the meat-and-cheese mixture and the other latke. Cut into quarters to serve.